Not really...but its effects do. Remember that AI's have no effect on estrogen already in your system, the only reduce the amount of new estrogen being converted. Your body still has to eliminate the existing estrogen on its own, and that takes time.
A SERM, by contrast, actually blocks the receptors so that circulating estrogen has nothing to bind to.
OP, it's best to take the AI from the beginning to prevent E2 issues.
HCG will take care of your atrophy, if it's bothering you. Otherwise, the boys will rebound fine after you recover. I think HCG is a "nice" thing to have on cycle but not essential. The best effect is that it keeps some of your natural production going, which makes PCT a breeze.